Question

Mohit invests Rs. 8,000 for 3 years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs. 9,440. Calculate: 

1. the rate of interest per annum.
2. the amount at the end of the second year.
3. the interest accrued in the third year.

Answer 1

Given:

Principal P = ₹ 8000

Amount after 1 year A₁ = ₹ 9440

(i) Rate of interest per annum

`A = P (1+r/100)`

`9440 = 8000 (1+r/100)`

`9440/8000 = 1+ r/100`

`1.18 = 1+r/100`

`r/100 = 0.18`

r = 18% per annum

(ii) Amount at the end of the second year

`A_2 = A_1 (1+r/100)`

A₂ ​= 9440 × 1.18

= ₹ 11139.20

​(iii) Interest accrued in the third year

A₃​ = A₂ ​× 1.18

= 11139.20 × 1.18

= ₹ 13144.26

Interest = A₃​ − A₂

​= 13144.26 − 11139.20

= ₹ 2005.06​